A combined finite element, boundary integral and spherical harmonic method for close-packed sonar arrays

Acoustic interactions within a sonar array are known to affect the array performance as well as the life expectancy of the transducers themselves. The ability to predict array performance is required for large close-packed arrays of acoustic transducers. In these cases, traditional full finite element or coupled finite element-boundary element methods prove costly. The general approach is to combine a single transducer finite element model with an analytic description of the surrounding fluid and neighboring transducers in the array. The finite element model produces the dynamic system matrix. The boundary integral equation relates surface pressure and velocity. Boundary elements are partitioned for the case of the surface of an arbitrary body circumscribed by a spherical surface to provide an implicit transfer of surface pressures to spherical fluid pressures and particle velocities. These quantities are then transformed in terms of spherical harmonics. The resulting series is combined with a spherical harmonic representation of the fluid using the addition theorem for multiple scatterers. This technique has been exercised to evaluate an array of electrically driven piezoelectric shell transducers. Results are compared to a coupled finite element-boundary element method